Other

We’ll
see how to calculate the
simple interest and the
compound
one in this article. We have to start with some
definitions, though.

Interest
is money paid by an individual or organization for the use of a sum of
money
called the principal.
The interest is usually paid at the end of specified
equal periods of time
(such as monthly, quarterly, or annually).

The
sum of the
principal and the interest is called the amount.

1.- Simple Interest

To help us work and calculate
the simple interest,
we have
these two easy formulas:

I = P r t
A = P + P r t

where
I = simple interest
P = principal
r = interest rate per year
t = time in years
A = amount

We can also conclude that
A = P(1 + r t) and
I = A - P

Examples

If an individual borrows
$1000 at 5% per year for 1.5 years,
how much interest must be paid on the loan?

I = P r t
I = 1000 (0.05) (1.5)
I = $75

If an organization
invests $13000 at 4% per year for 3
years, how much will the investment be worth at the end of the 3 years?

A = P + Prt
A = $13000 + $13000 (0.04) (3)
A = $14560

2.-
Compound Interest

Compound interest
means that the interest is paid
periodically over the term of the loan which results in a new principal
at the
end of each interval of time.

The ending balance is
given by:

where
A = amount, or ending balance
P = principal
r = annual interest rate
n = compounded times per year
t = number of years

The
following video shows an example and a solution using a calculator
specially prepared for such purpose. After the video, we show how to
solve the problem by creating in Matlab our own function for the task...

Let's
create our code! - Example

Find the amount of an
investment if $10,000 is invested at 5%
compounded monthly for three years.

Fortunately, we can
create a function in Matlab for the
compound interest formula, like this:

function A =
comp_int(P, r, n, t)
A = P*(1
+ r/n)^(n*t);

and we can call it from
another m-file, script, or from the
command window, in this way:

P =
10000;
r =
0.05;
n = 12;
t = 3;

format bankA
=
comp_int(P, r, n, t)

The answer is:

A = 11614.72

3.- Continuously Compounded Interest

When the interest is
compounded more frequently, we get to a
situation of continuously
compounded interest. This formula works it out: